Jan Steffen Müller

Code

Teaching

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Room 335
Phone: +49-40-42838-5189
E-Mail: jan(dot)steffen(dot)mueller(at)uni(minus)hamburg(dot)de
Office hour: By appointment

Research interests

Note that the pdf files are preprint versions which may differ from the published versions.

Explicit Kummer varieties of hyperelliptic Jacobian threefolds, Preprint (2012), submitted.	[pdf]	[arXiv]	[Magma-Code]
A height inequality for rational points on elliptic curves implied by the abc conjecture (with Ulf Kühn), Preprint (2012), submitted.	[pdf]	[arXiv]
A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties (with Jen Balakrishnan and William Stein), Preprint (2012), submitted.	[pdf]	[arXiv]
Lower bounds on the arithmetic self-intersection number of the relative dualizing sheaf on arithmetic surfaces (with Ulf Kühn), Preprint (2012), submitted.	[pdf]	[arXiv]
Computing canonical heights using arithmetic intersection theory, to appear in Math. Comp. (2012).	[pdf]	[arXiv]	[Magma-Code]
Local heights on elliptic curves and intersection multiplicities (with Vincenz Busch), Int. J. Number Theory 8, No. 6, 1477-1484 (2012).	[pdf]	[arXiv]
Computing canonical heights on Jacobians, PhD thesis, Department of Mathematics at Universität Bayreuth (2010).	[pdf]
Explicit Kummer surface formulas for arbitrary characteristic, LMS J. Comput. Math. 13, 47-64 (2010).	[pdf]	[arXiv]

A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties Arithmetic of L-functions, October 2012, University of Bristol	[pdf]
A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties Rational points on curves: A p-adic and computational perspective, September 2012, Oxford University	[pdf]
Computing canonical heights using arithmetic intersection theory Séminaire de Cryptographie de Rennes, December 2011, Université Rennes I	[pdf]
Algorithmische Aspekte der Vermutung von Birch und Swinnerton-Dyer (in German) Oberseminar Algebraische Geometrie, June 2011, LMU München	[pdf]
Arithmetik von Kummer Varietäten (in German) Oberseminar Algebra, February 2011, Universität Oldenburg	[pdf]
Computing canonical heights on Jacobians Rational points: Theory & Experiment, Workshop, May 2010, ETH Zürich	[pdf]
Explicit Kummer surface theory for arbitrary characteristic Rational points on curves and higher-dimensional varieties, June 2009, University of Warwick	[pdf]
For further talks see my cv.

Computing canonical heights on Jacobians of hyperelliptic curves over number fields using arithmetic intersection theory
- Magma-implementation of the algorithm described in Computing canonical heights using arithmetic intersection theory
- Part of the official Magma-distribution since version 2.18
Explicit formulas for Kummer varieties of Jacobians of hyperelliptic curves of genus 3
- Magma-Code for the paper Explicit Kummer varieties of hyperelliptic Jacobian threefolds

Winter term 2011/12
- Prep course for math students,
- Tutorials for linear algebra.
- Softwarepraktikum, Di 12-14 Uhr, Geom 142.
Sommer term 2011
- Tutorials for linear algebra.
- Exercise classes for linear algebra.
Winter term 2010/11
- Seminar on the arithmetic of elliptic curves.
- Tutorials for linear algebra.
- Prep course for math students.